Preheat your oven to 350°F and lightly grease a 9x13-inch baking dish with butter or cooking spray.
Season the chicken breasts evenly with kosher salt and black pepper, then heat olive oil in a large skillet over medium-high heat and cook the chicken for 6-7 minutes per side until golden brown and cooked through; let rest for 5 minutes before slicing into 1-inch pieces.
Steam the broccoli florets in a steamer basket over boiling water for 4-5 minutes until bright green and tender-crisp, then drain thoroughly and arrange in an even layer across the bottom of the prepared baking dish.
Melt the butter in a saucepan over medium heat, whisk in the flour, and cook for 1 minute until smooth and bubbly; gradually whisk in the milk and chicken broth until the sauce thickens enough to coat the back of a spoon, about 5-7 minutes.
Remove the saucepan from heat and stir in the Parmesan cheese, mayonnaise, lemon juice, and curry powder until the sauce is smooth and evenly combined.
Arrange the sliced chicken over the broccoli in the baking dish, pour the sauce evenly over the top, and sprinkle with shredded cheddar cheese.
Bake uncovered for 25-30 minutes until the casserole is bubbling around the edges and the cheese is melted and lightly golden brown on top.